Santini P
Institute of Theoretical Physics, University of Lausanne, CH-1015 Lausanne, Switzerland.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jan;61(1):93-9. doi: 10.1103/physreve.61.93.
Truncated Levy flights with correlated fluctuations of the variance (heteroskedasticity) are considered. A stylized model is introduced, in which the variance fluctuates between two possible values following a Markov chain process. Analogously to conventional truncated Levy flights with fixed variance, the central part of the probability distribution function of the increments at short time scales is found to be close to a Levy distribution. What makes these processes interesting is the fact that the crossover to the Gaussian regime may occur for times considerably larger than for uncorrelated (or no) variance fluctuations. Processes of this type may find direct application in the modeling of some economic time series, in which Levy scaling and heteroskedasticity are known to coexist.
考虑具有方差相关波动（异方差性）的截断列维飞行。引入了一个程式化模型，其中方差根据马尔可夫链过程在两个可能值之间波动。类似于具有固定方差的传统截断列维飞行，发现在短时间尺度上增量概率分布函数的中心部分接近列维分布。这类过程的有趣之处在于，与不相关（或无）方差波动相比，向高斯状态的转变可能发生在长得多的时间。这类过程可能直接应用于一些经济时间序列的建模，在这些序列中，已知列维标度和异方差性共存。
